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Sibirskii Zhurnal Industrial'noi Matematiki, 2013, Volume 16, Number 2, Pages 14–25 (Mi sjim776)  
This article is cited in 7 scientific papers (total in 7 papers)

Stability estimates for solutions to inverse extremal problems for the Helmholtz equation

G. V. Alekseevab, A. V. Lobanovc

a Vladivostok State University of Economics and Service, 41 Gogol st., 690014 Vladivostok, Russia
b Far Eastern Federal University, 8 Sukhanov st., 690950 Vladivostok, Russia
c Institute of Applied Mathematics, 7 Radio st., 690041 Vladivostok, Russia
Full-text PDF (276 kB) Citations (7)
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Abstract: Inverse problems for the Helmholtz equation of the acoustic scattering on a three-dimensional inclusion are considered. Using an optimization method, we reduce these problems to inverse extremal problems in which the role of controls is played by a variable refraction index and boundary source density. Solvability of these problems is proved and some optimality systems are obtained that describe necessary optimality conditions. Basing on the analysis of the optimality systems, sufficient conditions on the input data are deduced that guarantee the uniqueness and stability of optimal solutions.
Keywords: Helmholtz equation, scattering problem, inhomogeneous medium, multiplicative control, inverse problem, uniqueness, stability.
Received: 19.02.2013
English version:
Journal of Applied and Industrial Mathematics, 2013, Volume 7, Issue 3, Pages 302–312
DOI: https://doi.org/10.1134/S1990478913030034
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: G. V. Alekseev, A. V. Lobanov, “Stability estimates for solutions to inverse extremal problems for the Helmholtz equation”, Sib. Zh. Ind. Mat., 16:2 (2013), 14–25; J. Appl. Industr. Math., 7:3 (2013), 302–312
Citation in format AMSBIB
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\by G.~V.~Alekseev, A.~V.~Lobanov
\paper Stability estimates for solutions to inverse extremal problems for the Helmholtz equation
\jour Sib. Zh. Ind. Mat.
\yr 2013
\vol 16
\issue 2
\pages 14--25
\mathnet{http://mi.mathnet.ru/sjim776}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3203338}
\transl
\jour J. Appl. Industr. Math.
\yr 2013
\vol 7
\issue 3
\pages 302--312
\crossref{https://doi.org/10.1134/S1990478913030034}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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